Traveling Band Solutions in a System Modeling Hunting Cooperation

Abstract

A classical Lotka–Volterra model with the logistical growth of prey-and-hunting cooperation in the functional response of predators to prey was extended by introducing advection terms, which included the velocities of animals. The effect of velocity on the kinetics of the problem was analyzed. In order to examine the band behavior of species over time, traveling wave solutions were introduced, and conditions for the coexistence of both populations and/or extinction were found. Numerical simulations illustrating the obtained results were performed.

Keywords

• hunting cooperation
• predator–prey
• stability
• advection terms
• traveling bands